{
  "abstract": "We present linear codes with parameters [88,8,64] and [90,8,65] over GF(7), [98,7,75] and [97,8,72] over GF(8), and [44,7,31] over GF(9). Each has a minimum distance one larger than the lower bound listed in Grassl's tables of best known linear codes; codes with parameters [89,8,64] over GF(7) and [96,8,71], [95,8,70], [94,8,69] over GF(8) follow. Four of the five codes are obtained from a quasi-cyclic code and a vector that is constant on each block, by Construction X with a repetition code. The remaining one, the [90,8,65] code, is obtained from the first by appending two coordinates. The parameters and all weight counts were obtained by exhaustive enumeration, and a short program that repeats these computations is included.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.14433",
  "author_total": 1,
  "authors": [
    {
      "name": "Sebastian Cochinescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/037cg2ffg5v7s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.14433",
  "fulltext_url": null,
  "id": "037cg2ffg5v7s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.14433",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.14433",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-10",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/037cg2ffg5v7s.ris",
  "sources": [
    {
      "first_seen": "2026-11-11T06:21:55Z",
      "native_id": "2611.14433",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.14433"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    }
  ],
  "title": "New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X",
  "title_text": "New linear codes over GF(7), GF(8) and GF(9) from quasi-cyclic codes and Construction X",
  "type": "preprint",
  "updated_at": "2026-11-13T06:20:56Z",
  "url": "https://research.draconitic.com/paper/037cg2ffg5v7s",
  "venue": "arXiv",
  "versions": []
}